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We present a detailed report of the method, setup, analysis and results of aprecision measurement of the positive muon lifetime. The experiment wasconducted at the Paul Scherrer Institute using a time-structured, nearly100%-polarized, surface muon beam and a segmented, fast-timing, plasticscintillator array. The measurement employed two target arrangements; amagnetized ferromagnetic target with a ~4 kG internal magnetic field and acrystal quartz target in a 130 G external magnetic field. Approximately 1.6 x10^{12} positrons were accumulated and together the data yield a muon lifetimeof tau_{mu}(MuLan) = 2196980.3(2.2) ps (1.0 ppm), thirty times more precisethan previous generations of lifetime experiments. The lifetime measurementyields the most accurate value of the Fermi constant G_F (MuLan) = 1.1663787(6)x 10^{-5} GeV^{-2} (0.5 ppm). It also enables new precision studies of weakinteractions via lifetime measurements of muonic atoms.

Detailed Report of the MuLan Measurement of the Positive Muon Lifetime and Determination of the Fermi Constant